Search NASA⌕ Search

SEARCH · Search NASA

Results for “FORMULAS - LOADS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Simple formulas for designing an offset multibeam parabolic reflector

Theoretical methods (computer programs) which are available for analyzing reflector performance are of the 'forward' type. Performance parameters can be calculated after the configuration of the reflector is given. In many practical applications, however, the problem is often of the 'inverse' type. The reflector has to be designed on the basis of a given set of performance parameters. Attention is given to a systematic procedure based on simple formulas for solving such an inverse problem. Because of the simplicity of the formulas, the final results obtained from the procedure do not have great accuracy. Thus, they represent only a preliminary design, which can be refined by repeatedly using the forward-type programs.

Lee, S.-W.↗
NASA NTRS1981

Geometrically derived difference formulae for the numerical integration of trajectory problems

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

Mcleod, R. J. Y.↗
NASA NTRS1986

An approximation formula for a class of fault-tolerant computers

An approximation formula is derived for the probability of failure for fault-tolerant process-control computers. These computers use redundancy and reconfiguration to achieve high reliability. Finite-state Markov models capture the dynamic behavior of component failure and system recovery, and the approximation formula permits an estimation of system reliability by an easy examination of the model.

White, A. L.↗
NASA NTRS1988

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Badavi, Forooz F.↗
NASA NTRS1990

An estimating formula for ion-atom association rates in gases

A simple estimating formula is derived for rate coefficients of three-body ion atom association in gases and compare its predictions to experimental data on ion association and three-body radiative charge transfer reactions of singly- and doubly-charged rare-gas ions. The formula appears to reproduce most experimental data quite well. It may be useful for estimating the rates of reactions that have not been studied in the laboratory.

Chatterjee, B. K.↗
NASA NTRS1991

On the position of the near-earth neutral sheet - A comparison of magnetic model predictions with empirical formulas

A detailed comparison of the near-earth neutral sheet position according to several approximations has been made. In particular, two empirical formulas for the neutral sheet location, recently derived from AMPTE/CCE data, have been compared with the corresponding positions derived from Tsyganenko's magnetic field models. Cylindrical coordinates referenced to the geodipole have been used, and the position of the neutral sheet has been identified by the reversal of the radial component of the magnetic field. The analysis reveals that, in the region X(GSM) = -9 to -5 earth radii, abs. value of Y(GSM) not greater than 5 earth radii, close agreement exists between the empirical formulas and the Tsyganenko models. Furthermore, the Tsyganenko models provide a representation for the neutral sheet position in the transition region between near-earth and distant tail models.

Peredo, Mauricio↗
NASA NTRS1954

Formulas for the elastic constants of plates with integral waffle-like stiffening

Formulas are derived for the fifteen elastic constants associated with bending, stretching, twisting, and shearing of plates with closely spaced integral ribbing in a variety of configurations and proportions. In the derivation the plates are considered, conceptually, as more uniform orthotropic plates somewhat on the order of plywood. The constants, which include the effectiveness of the ribs for resisting deformations other than bending and stretching in their longitudinal directions, are defined in terms of four coefficients, and theoretical and experimental methods for the evaluation of these coefficients are discussed. Four of the more important elastic constants are predicted by these formulas and are compared with test results. Good correlation is obtained. (author)

Dow, Norris R↗
NASA NTRS1933

General formulas and charts for the calculation of airplane performance

This report presents general formulas for the determination of all major airplane performance characteristics. A rigorous analysis is used, making no assumption regarding the attitude of the airplane at which maximum rate of climb occurs, but finding the attitude at which the excess thrust horsepower is maximum. Equations and charts are developed which show the variation of performance due to a change in any of the customary design parameters. Performance determination by use of the formulas and charts is rapid and explicit. The results obtained by this performance method have been found to give agreement with flight tests that is, in general, equal or superior to results obtained by present commonly used methods.

Oswald, W Bailey↗
NASA NTRS1953

Charts and approximate formulas for the estimation of aeroelastic effects of the lateral control of swept and unswept wings

Charts and approximate formulas are presented for the estimation of static aeroelastic effects on the spanwise lift distribution, rolling-moment coefficient, and rate of roll due to the deflection of ailerons on swept and unswept wings at subsonic and supersonic speeds. Some design considerations brought out by the results of this report are discussed. This report treats the lateral-control case in a manner similar to that employed in NACA Report 1140 for the symmetric-flight case, and is intended to be used in conjunction with NACA Report 1140 and the charts and formulas presented therein.

Foss, Kenneth A↗
NASA NTRS1994

ASU Formula Lightning Race Vehicle Report Prepared for Ohio Aerospace Institute

This report describes the drive system in the Arizona State University Formula Lightning electric race car when it participated in the 1994 Cleveland Electric Formula Classic on 9 July 1994. In addition, the telemetry system used to monitor the car's performance and plans for improving the car's performance are described.

Sirkis, Murray D.↗
NASA NTRS1998

Conditions for Aeronomic Applicability of the Classical Electron Heat Conduction Formula

Conditions for the applicability of the classical formula for heat conduction in the electrons in ionized gas are investigated. In a fully ionised gas ( V(sub en) much greater than V(sub ei)), when the mean free path for electron-electron (or electron-ion) collisions is much larger than the characteristic thermal scale length of the observed system, the conditions for applicability break down. In the case of the Venus ionosphere this breakdown is indicated for a large fraction of the electron temperature data from altitudes greater than 180 km, for electron densities less than 10(exp 4)/cc cm. In a partially ionised gas such that V(sub en) much greater than V(sub ei) there is breakdown of the formula not only when the mean free path of electrons greatly exceeds the thermal scale length, but also when the gradient of neutral particle density exceeds the electron thermal gradient. It is shown that electron heat conduction may be neglected in estimating the temperature of joule heated electrons by observed strong 100 Hz electric fields when the conduction flux is limited by the saturation flux. The results of this paper support our earlier aeronomical arguments against the hypothesis of planetary scale whistlers for the 100 Hz electric field signal. In turn this means that data from the 100 Hz signal may not be used to support the case for lightning on Venus.

Cole, K. D.↗
NASA NTRS2004

Quantification of Inlet Impedance Concept and a Study of the Rayleigh Formula for Noise Radiation from Ducted Fan Engines

This paper addresses two aspects of duct propagation and radiation which can contribute to more efficient fan noise predictions. First, we assess the effectiveness of Rayleigh's formula as a ducted fan noise prediction tool. This classical result which predicts the sound produced by a piston in a flanged duct is expanded to include the uniform axial inflow case. Radiation patterns using Rayleigh's formula with single radial mode input are compared to those obtained from the more precise ducted fan noise prediction code TBIEM3D. Agreement between the two methods is excellent in the peak noise regions both forward and aft. Next, we use TBIEM3D to calculate generalized radiation impedances and power transmission coefficients. These quantities are computed for a wide range of operating parameters. Results were obtained for higher Mach numbers, frequencies, and circumferential mode orders than have been previously published. Viewed as functions of frequency, calculated trends in lower order inlet impedances and power transmission coefficients are in agreement with known results. The relationships are more oscillatory for higher order modes and higher Mach numbers.

Posey, Joe W.↗
NASA NTRSDate not supplied

DDFRG: Double Differential FRaGmentation Models for Proton and Light Ion Production in High Energy Nuclear Collisions: Closed Form, Analytic Formulas for Transport Codes and other Applications

New models for Double-Differential FRaGmentation (DDFRG) cross sections for proton and light ion production from high energy nucleus-nucleus collisions are developed. The proton model employs thermal production from the projectile, central fireball and target sources, and also quasi-elastic direct knockout production. Light ion production cross sections employ a hybrid coalescence model. The models are able to describe a wide range of experimental data with only a limited set of model parameters. Closed form analytic formulas for double-differential cross sections as well as single-differential energy cross sections are developed. The analytic formulas enable highly efficient computation for space radiation transport codes and other applications.

John W Norbury↗